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arXiv · 1803.09370

Popular Matching in Roommates Setting is NP-hard

Sushmita Gupta·Pranabendu Misra·Saket Saurabh·Meirav Zehavi
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Abstract

An input to the Popular Matching problem, in the roommates setting, consists of a graph $G$ and each vertex ranks its neighbors in strict order, known as its preference. In the Popular Matching problem the objective is to test whether there exists a matching $M^\star$ such that there is no matching $M$ where more people are happier with $M$ than with $M^\star$. In this paper we settle the computational complexity of the Popular Matching problem in the roommates setting by showing that the problem is NP-complete. Thus, we resolve an open question that has been repeatedly, explicitly asked over the last decade.

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Sushmita Gupta, Pranabendu Misra, Saket Saurabh, Meirav Zehavi. 2018-03-25. Popular Matching in Roommates Setting is NP-hard. https://arxiv.org/abs/1803.09370

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